Homological representations of the Iwahori–Hecke algebra

Stephen Bigelow
2004 Geometry and Topology Monographs   unpublished
Representations of the Iwahori-Hecke algebra of type A n−1 are equivalent to representations of the braid group B n for which the generators satisfy a certain quadratic relation. We show how to construct such representations from the natural action of B n on the homology of configuration spaces of the punctured disk. We conjecture that all irreducible representations of H n can be obtained in this way, even for non-generic values of q .
doi:10.2140/gtm.2004.7.493 fatcat:unbf6ivkgbhphacucpluemcfdu